The equation of the tangent at the $(9, 6)$ on the parabola $y^{2} = 4 x$

x-3y+9=0

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9x-2y+69=0

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2x+9y-69=0

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9x+2y-69=0

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Solution

The correct option is B x-3y+9=0
The equation of Parabola $y^{2} = 4 x$
Point $(9, 6)$
Slope of tangent $2 y \frac{d y}{d x} = 4 \frac{d y}{d x} = \frac{2}{y} {\frac{d y}{d x} ∣ ∣ ∣}_{(9, 6)} = \frac{1}{3}$
Equation of tangent
$y - 6 = \frac{1}{3} (x - 9) x - 3 y + 9 = 0$

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The equation of the tangent at the (9,6) on the parabola y2=4x

The correct option is B x-3y+9=0The equation of Parabola y2=4xPoint (9,6) Slope of tangent 2ydydx=4dydx=2ydydx∣∣∣(9,6)=13Equation of tangenty−6=13(x−9)x−3y+9=0

The equation of the tangent at the $(9, 6)$ on the parabola $y^{2} = 4 x$

The correct option is B x-3y+9=0
The equation of Parabola $y^{2} = 4 x$
Point $(9, 6)$
Slope of tangent $2 y \frac{d y}{d x} = 4 \frac{d y}{d x} = \frac{2}{y} {\frac{d y}{d x} ∣ ∣ ∣}_{(9, 6)} = \frac{1}{3}$
Equation of tangent
$y - 6 = \frac{1}{3} (x - 9) x - 3 y + 9 = 0$